"He is shedding a little." Somehow (I'm not a grammarian!), when we put "a little" after "shedding," it works as an adverb. He is shedding. How much is he shedding? He is shedding a little. If we put it before, when I hear "He is a little..." I do not expect to hear any form of verb. I expect to hear something like: "He is a little Boston terrier," or "He is a little sleepy today."

Also, we do use the verb "to shed" when talking about cats, dogs, horses, etc.

He/she is shedding a little.